## Quiz on Laplace Transforms

1. What is 2 y(t) in Laplace domain?

A. 2 \delta(t)
Incorrect. The impulse function 2 \delta(t) is from the inverse Laplace transform of the number 2
B. 2 Y(s)
Correct. The Laplace transform of a time domain variable y(t) is the same variable but in the Laplace domain Y(s).
C. Y(s) y(t)
Incorrect. Laplace domain (s) and time domain (t) functions never appear together
D. Y(s)^2
Incorrect. The conversion to Laplace domain is not integration

2. What is the Laplace transform of {d^2f}/{dt^2} with f(0) = 1 and f'(0) = 2?

A. s^2F(s) - 2s -1
Incorrect. The solution is s^2 F(s) - s f(0) - f'(0)
B. 2sF(s) - 2s -2
Incorrect. The solution is s^2 F(s) - s f(0) - f'(0)
C. s^2F(s) - s -2
Correct. The solution is s^2 F(s) - s f(0) - f'(0)
D. s^2F(s) - s + 2
Incorrect. The sign before the f'(0) should be negative

3. What is the initial and final value of Y(s) = {(s + 3)}/{s(2s + 5)(3s + 6)}?

A. Initial: 1, Final: 1/10
Incorrect. Use IVT: y_0 = \lim_{s \to \infty} s Y(s) and FVT: y_\infty = \lim_{s \to 0} s Y(s)
B. Initial: 1, Final: 0
Incorrect. Use IVT: y_0 = \lim_{s \to \infty} s Y(s) and FVT: y_\infty = \lim_{s \to 0} s Y(s)
C. Initial: 0, Final: 1
Incorrect. Use IVT: y_0 = \lim_{s \to \infty} s Y(s) and FVT: y_\infty = \lim_{s \to 0} s Y(s)
D. Initial: 0, Final: 1/10
Correct.
IVT: y_0 = \lim_{s \to \infty} s Y(s)= (\infty+3) / {(2*\infty+5)(3*\infty+6)} = 0
FVT: y_\infty = \lim_{s \to 0} s Y(s) = 3/{(5)(6)} = 1/{10}